The invention concerns a corrector for axial and off-axial beam paths of a particle-optical system, comprising a first and a second correction piece, which are successively disposed in the beam path on an optical axis, wherein each correction piece comprises four successive multipole elements disposed symmetrically with respect to a center plane and with the following fields, wherein the first and the fourth multipole elements are used to generate quadrupole fields, and the second and the third multipole elements are used to generate octupole fields and quadrupole fields, wherein the latter are superposed magnetic and electric fields, and wherein the quadrupole fields of all four multipole elements are successively rotated from one to the other through 90°, such that chromatic aberration correction can be performed through interaction between the magnetic and electric fields using astigmatic intermediate images in the second and third multipole elements, and aperture aberration correction can be performed using the quadrupole fields and the octupole fields. The invention also concerns a transmission electron microscope comprising a corrector of this type.
Particle-optical systems are advantageous compared to light optics in that they provide a considerably better resolution due to the shorter wavelength of electrons and ions. Achieving the theoretically possible resolution limit of half a wavelength is complicated by the fact that the lenses that are used operate with magnetic or electric fields and exhibit numerous lens aberrations.
Such lens aberrations can be subdivided into chromatic aberrations and geometrical image aberrations. The chromatic aberrations are caused by the fact that the imaging electrons or ions have different velocities and therefore different wavelengths. This is mainly due to the fact that the electrons (or ions) emitted for generating the beam have a certain energy beam width.
The geometrical image aberrations are mainly due to inaccurate imaging by the electromagnetic fields which must obey the Laplace equation. This produces aperture aberrations because the focal length of the outer lens zones is smaller than that of the inner lens zones. In consequence thereof, a point in the image plane is no longer imaged as a point. A further source of aberrations results from the fact that the lenses are not completely symmetrical and therefore the strength of the lenses differs in two directions perpendicular to the optical axis. This aberration is called astigmatism. There are, however, further image aberrations, the cause of which is not always known.
Image aberrations occur in the form of axial image aberrations when an axial point is imaged. The beam dependence for imaging the latter, is determined by the dependence of the axial fundamental paths xα and yβ that start from the axial point of the object plane and lie in the x and y sections. Image aberrations also occur in the form of off-axial image aberrations for imaging an off-axial image point. The beam path for off-axial imaging is determined by the dependence of the off-axial fundamental paths xγ and yδ that start from a point on the object plane at some distance to the axis, and lie in the x- and y section.
Due to the diffraction dependence of the beams, these aberrations occur in several orders. The geometrical image aberrations are thereby visible in the form of characteristic aberration figures that surround the axis. These occur e.g. from second to fifth order in the form of the following aberrations: second order: three-fold axial astigmatism, axial coma, third order: four-fold axial astigmatism, aperture aberration, axial star aberration, fourth order: five-fold axial astigmatism, axial coma, axial trilobe aberration, fifth order: six-fold axial astigmatism, aperture aberration, axial star aberration, axial rosette aberration, . . . etc. The multiplicity thereby indicates the number of star corners of the associated image aberration figure. Aberrations starting from fourth order are also called aberrations of higher order.
Geometrical image aberrations are mainly caused by the objective lens, but also by other lenses and by the corrector itself. These aberrations are corrected by the corrector through downstream as well as upstream compensation, wherein the correction measure always depends on the result of the final image.
The basis for the correction of the axial image aberrations are the findings of O. Scherzer (O. Scherzer: “Sphärische und chromatische Korrektur von Elektronen-Linsen” (spherical and chromatic correction of electron lenses), OPTIK, DE, JENA, 1947, pages 114-132, XP002090897, ISSN: 0863-0259), that show that the correction of spherical (i.e. geometrical) and chromatic (i.e. color) aberrations is possible for particle beams by using non-rotationally symmetrical fields. Astigmatic intermediate images are thereby generated and correction is successively performed in an intermediate image in the x plane, and then in an intermediate image in the y plane which is perpendicular thereto. The eccentricity of the beam is subsequently eliminated again by reuniting it into a round beam. O. Scherzer establishes the conditions required to achieve these corrections (loc. cit.). These conditions, which are called the Scherzer theorem, form the basis of any axial aberration correction in particle optics. The correction of off-axial aberrations requires no astigmatic intermediate images. It can be performed with round or multipole fields.
For correcting non-round aberrations, such as e.g. astigmatism, a non-round field is required in order to restore the beam to its round cross-section, e.g. in the case of astigmatism, or to counteract non-roundness causing other non-round aberrations.
Departing therefrom, Rose (Optik, Volume 34, 1971, pages 285-311, in particular to page 293) proposes a corrector of the above-mentioned type that achieves relatively extensive aperture correction, wherein the corrector itself produces almost no aberrations. This corrector, however, was not further examined, since it is disadvantageous compared to other proposals made therein. In particular, the astigmatism of third order would be difficult to eliminate with the corrector of the above-mentioned type, thereby unavoidably causing aberrations of higher order.
It is therefore the underlying purpose of the invention to also eliminate the astigmatism of third order without introducing disturbing aberrations of higher order. Moreover, additional measures are taken for eliminating aberrations up to higher orders in order to achieve a satisfactory image resolution of up to approximately 5000 image points along an image diameter.